Computerized X-ray apparatus such as CT scanners use a plurality of processors to obtain desired tomographs. The scientists who design such equipment are continuously seeking ways and means for reducing the quantity of computations required to obtained the tomograph while striving to maintain high picture fidelity of good resolution with minimal artifacts. Such designers continuously compromise between complexity or quantity of computations required and the quality of the tomograph. Such compromises are found, for example, in U.S. Pat. Nos. Re 30,947, 4,075,492, and 4,570,224. The aforementioned patents are concerned with CT scanners that use divergent beams radiating from a source of X-rays. Using divergent beams instead of parallel beams inherently requires many more computations to reconstruct an image. Rather than proceeding with the significantly greater number of computations required with divergent beams, the above patents offer the compromise solution of "re-ordering" the divergent rays (or fan beams) to parallel rays or views.
However, the spacing between samples obtained by the re-ordering process is laterally unequal. The unequal spacing results in artifacts (diminution of picture quality). The prior art approaches to reconstruction techniques when the X-ray sources provided divergent beams have traditionally followed three techniques, which are:
1. Using special divergent beam backprojecting or reconstruction algorithms based on the divergent beam geometry scanners;
2. Reordering the raw data into parallel beam shadowgraph data with non-equal spacing then rebinning the non-equal spacing into parallel equal space shadowgraph data and then applying preprocessing filtering and backprojecting algorithms based on the parallel beam, equal space scanner geometry; and
3. Reordering the raw data into two separate sets, the first set is rebinned to enable pre-processing based on parallel beam equal spaced scanner geometry followed by modified filtering and backprojecting. The rebinned, re-ordered first set is operated on during the rebinning, etc. to assume a spacing which counteracts the unequal spacing of the re-ordered raw data of the second set. The recombined sets thus provides high quality images with reduced computational steps.
There are explicit drawbacks inherent in each of the above implementations. They are increased mechanical complexity, increased computation time, or spatial resolution that is reduced to below that theoretically possible; and increased image artifacts as a result of the approximations in the algorithms.
The use of the mathematically correct algorithms of the first technique for pre-processing filtering and backprojecting based on the divergent beam geometry of the scanners would result in images which have no reduction from the theoretically possible spatial resolution, and have a minimum of artifacts. However, the first technique is mathematically complex and requires a relatively large amount of computation time.
The second technique, that is the rebinning by interpolation to convert the unequal lateral spacing to the equal lateral spacing converts the fan beam geometry to parallel beam geometry. The conversion reduces the number of computations in the reconstruction algorithm. However, the rebinning process introduces a smoothing effect and significantly reduces the system's spatial resolution.
The third technique is the most efficient from the computation time aspect. However, the geometric approximations may introduce image artifacts as well as reduce spatial resolution.
Accordingly, there exists a problem for which a complete solution still has escaped the experts and proven elusive. That is, the need for a method and system for reconstructing images using parallel reconstruction algorithms when the data is obtained from CT scanners using divergent beam geometry.
According to the present invention the sought after solution is to provide a method for detecting, modifying, and rearranging divergent beam derived data to obtain tomographic images with maximum spatial resolution and minimum artifacts in a relatively short time, that is, by reducing computation quantities and/or time to a minimum.
In accordance with a preferred broad aspect of the present invention, a method of detecting, modifying and rearranging divergent beam derived data to obtain tomographic images having maximum spatial resolution and minimum artifacts using a reduced number of computations is provided, said method comprises the steps of:
directing divergent beams of penetrating radiation through a body being examined from source means on one side of said body to detector means on the other side of said body, PA1 angularly displacing the divergent beams and detectors relative to the body, PA1 detecting radiation that is passed through the body at a number of angularly spaced positions within the angle subtended by the divergent beams, PA1 determining sets of detected radiation data representative of the plurality of angularly and laterally spaced shadowgrams indicative of the transmission of radiation through the body, PA1 reordering said data that correspond to determined sets of detected radiation data into data corresponding to parallel projections, the spacing between projections being laterally unequal, PA1 filtering the reordered data, PA1 rebinning the reordered, filtered data to obtain equal laterally spaced parallel filtered data, and PA1 backprojecting said equal laterally spaced parallel filtered data to form tomographic images.
A feature of the invention provides for rebinning at a density that is greater than half the Nyquist criterion.
A related feature of the invention provides for rebinning at density equal to the Nyquist criterion.
Yet another feature of the invention provides for making corrections on pre-processed data to prevent cupping and dishing artifacts.
Another feature of the invention provides for making a correction to assure that the tomographic image has the correct CT numbers. This last correction uses a rating function which is related to the geometry of the particular tomographic equipment used in obtaining the image. This feature provides for obtaining the correction factor to be used in assuring the correct CT number of the output data by determining a relationship between the integrals of a view data using fan beam correction and using true rebinning.